I think that the election of a pope is restricted to Roman Rite Cardinals as candidates, The pope is the Bishop of Rome, his See is in Rome, it would not make sense if say, a Greek Catholic Cardinal was elected the Bishop of the See of Rome, because he is not of the Roman Rite
Actually it would make perfectly good sense from both a theological and eccesiological point of view. In olden times (I just love saying that

), there were several Easterners and Orientals on the papal throne. The position was then, as it is now, Bishop of Rome, and a non-westerner was not a problem. Of course times were simpler then, but even so, there is nothing to prevent an Oriental or Eastern bishop from being elected.
Could it happen? Yes. Is it
going to happen? Highly doubtful.
This same issue was discussed a couple of months back in another thread (in, I think, the Eastern Catholicism forum). In any case, if an Eastern or Oriental bishop were to be elected, it would, IMHO, present
practical questions, but nothing that could not be surmounted in a reasonable manner.
Case in point: the Pope is Bishop of Rome. But of course he is more than that: he is also head of the
Universal Church. Yet, at the same time, the people of the Diocese of Rome should have an ordinary, just like any other diocese. Hence we have the Vicar for Rome who functions
ad nutum as the de facto ordinary. There is no reason something similar could not be done to manage affairs particular to the West in general (despite the official abrogation of the title “Patriarch of the West,” the Bishop of Rome is still that, in fact, and has always been). He simply delegates (and remember, the delegation is
ad nutum so it could be revoked in an instant) those responsibilities, all the while retaining full authority.
Could this happen? Yes? Is it likely? No. I only bring it up to reinforce the fact that there is nothing (absolutely
nothing) that would prevent an Eastern or Oriental bishop from election to the Papacy.